Probability Guide

There are a lot of numbers that are hidden from the players in Metroplexity, but most are able to be determined with reasonable certainty, and many with complete certainty.

Collecting samples for complete certainty

A few example of hidden complete certainty numbers:

  • Opponent's HP: If you can deal 49 damage and opponent is not dead, but deal 50 damage and opponent is dead, you can safely conclude that opponent has 50 HP (barring further complications).
  • Opponent's Defenses: If your Melee attack does 3-6 damage, you can be certain of opponent's Melee Defense (barring further complications like Reactive Defense).

These numbers can be calculated with 100% certainty, but can sometimes take a very long time to determine.

Collecting samples to be reasonable sure that an event didn't happen

A flip-side to the above is trying to figure out a number range by randomly selecting numbers from it. A few examples:

  • Food consumption range: all foods give an amount of energy between X and Y randomly selected.
  • Opponent's attacks limited by their Attribute: will give a range of (Opp Attack-Player Defense) and (Opp Attack - [something modified by attribute]—fix this)

These are impossible to conclusively determine but can be nailed to with reasonable certainty by repeated samples. For example: A food item is eaten many times. The data gives {2,3,4,3,4,2,3,2,4,2,4,2,4,3,4,2,4,2,4,2,4,3,4,3,4,2,3,3,4} energy as data points. The observed range is 2-4 energy. It is likely the theoretical range is also 2-4 energy, but it is still possible that the range is 2-5 energy and we were unlucky with our sampling so far.

The chart below shows the number of data points needed to be 95% or 99% reasonably sure that you have all the possible data points.

Data range found so far 95%* 99%*
1 6 8
2 11 15
3 16 21
4 21 28
5 27 36
6 33 43
7 38 51
8 44 58
9 51 66
10 57 74
11 63 82
12 70 90
13 76 98
14 83 106
15 90 115
20 124 157
25 159 201
30 196 ~250

Collecting data samples to determine a chance event.

For example: concluding that an item drops 30%, 35% or 40% of the time.
(to do)

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